{"id":"https://openalex.org/W2084633140","doi":"https://doi.org/10.1142/s021819670700355x","title":"NORMALIZED EXPRESSIONS AND FINITE AUTOMATA","display_name":"NORMALIZED EXPRESSIONS AND FINITE AUTOMATA","publication_year":2007,"publication_date":"2007-02-01","ids":{"openalex":"https://openalex.org/W2084633140","doi":"https://doi.org/10.1142/s021819670700355x","mag":"2084633140"},"language":"en","primary_location":{"id":"doi:10.1142/s021819670700355x","is_oa":false,"landing_page_url":"https://doi.org/10.1142/s021819670700355x","pdf_url":null,"source":{"id":"https://openalex.org/S23260266","display_name":"International Journal of Algebra and Computation","issn_l":"0218-1967","issn":["0218-1967","1793-6500"],"is_oa":false,"is_in_doaj":false,"is_core":true,"host_organization":"https://openalex.org/P4310319815","host_organization_name":"World Scientific","host_organization_lineage":["https://openalex.org/P4310319815"],"host_organization_lineage_names":["World Scientific"],"type":"journal"},"license":null,"license_id":null,"version":"publishedVersion","is_accepted":true,"is_published":true,"raw_source_name":"International Journal of Algebra and Computation","raw_type":"journal-article"},"type":"article","indexed_in":["crossref"],"open_access":{"is_oa":false,"oa_status":"closed","oa_url":null,"any_repository_has_fulltext":false},"authorships":[{"author_position":"first","author":{"id":"https://openalex.org/A5111844760","display_name":"Jean-Marc Champarnaud","orcid":null},"institutions":[{"id":"https://openalex.org/I4210108118","display_name":"Laboratoire d'Informatique, du Traitement de l'Information et des Syst\u00e8mes","ror":"https://ror.org/01f1vfy95","country_code":"FR","type":"facility","lineage":["https://openalex.org/I141576021","https://openalex.org/I4210105918","https://openalex.org/I4210105918","https://openalex.org/I4210105918","https://openalex.org/I4210108118","https://openalex.org/I62396329","https://openalex.org/I88814501"]},{"id":"https://openalex.org/I62396329","display_name":"Universit\u00e9 de Rouen Normandie","ror":"https://ror.org/03nhjew95","country_code":"FR","type":"education","lineage":["https://openalex.org/I4210105918","https://openalex.org/I62396329"]}],"countries":["FR"],"is_corresponding":false,"raw_author_name":"J.-M. CHAMPARNAUD","raw_affiliation_strings":["LITIS, University of Rouen, 76000 Saint-Etienne du Rouvray, France"],"raw_orcid":null,"affiliations":[{"raw_affiliation_string":"LITIS, University of Rouen, 76000 Saint-Etienne du Rouvray, France","institution_ids":["https://openalex.org/I4210108118","https://openalex.org/I62396329"]}]},{"author_position":"middle","author":{"id":"https://openalex.org/A5072626701","display_name":"Fa\u00efssal Ouardi","orcid":"https://orcid.org/0000-0002-7636-5001"},"institutions":[{"id":"https://openalex.org/I4210108118","display_name":"Laboratoire d'Informatique, du Traitement de l'Information et des Syst\u00e8mes","ror":"https://ror.org/01f1vfy95","country_code":"FR","type":"facility","lineage":["https://openalex.org/I141576021","https://openalex.org/I4210105918","https://openalex.org/I4210105918","https://openalex.org/I4210105918","https://openalex.org/I4210108118","https://openalex.org/I62396329","https://openalex.org/I88814501"]},{"id":"https://openalex.org/I62396329","display_name":"Universit\u00e9 de Rouen Normandie","ror":"https://ror.org/03nhjew95","country_code":"FR","type":"education","lineage":["https://openalex.org/I4210105918","https://openalex.org/I62396329"]}],"countries":["FR"],"is_corresponding":false,"raw_author_name":"F. OUARDI","raw_affiliation_strings":["LITIS, University of Rouen, 76000 Saint-Etienne du Rouvray, France"],"raw_orcid":null,"affiliations":[{"raw_affiliation_string":"LITIS, University of Rouen, 76000 Saint-Etienne du Rouvray, France","institution_ids":["https://openalex.org/I4210108118","https://openalex.org/I62396329"]}]},{"author_position":"last","author":{"id":"https://openalex.org/A5033485939","display_name":"Djelloul Ziadi","orcid":"https://orcid.org/0000-0001-5497-0828"},"institutions":[{"id":"https://openalex.org/I4210108118","display_name":"Laboratoire d'Informatique, du Traitement de l'Information et des Syst\u00e8mes","ror":"https://ror.org/01f1vfy95","country_code":"FR","type":"facility","lineage":["https://openalex.org/I141576021","https://openalex.org/I4210105918","https://openalex.org/I4210105918","https://openalex.org/I4210105918","https://openalex.org/I4210108118","https://openalex.org/I62396329","https://openalex.org/I88814501"]},{"id":"https://openalex.org/I62396329","display_name":"Universit\u00e9 de Rouen Normandie","ror":"https://ror.org/03nhjew95","country_code":"FR","type":"education","lineage":["https://openalex.org/I4210105918","https://openalex.org/I62396329"]}],"countries":["FR"],"is_corresponding":false,"raw_author_name":"D. ZIADI","raw_affiliation_strings":["LITIS, University of Rouen, 76000 Saint-Etienne du Rouvray, France"],"raw_orcid":null,"affiliations":[{"raw_affiliation_string":"LITIS, University of Rouen, 76000 Saint-Etienne du Rouvray, France","institution_ids":["https://openalex.org/I4210108118","https://openalex.org/I62396329"]}]}],"institutions":[],"countries_distinct_count":1,"institutions_distinct_count":3,"corresponding_author_ids":[],"corresponding_institution_ids":[],"apc_list":null,"apc_paid":null,"fwci":1.4966,"has_fulltext":false,"cited_by_count":18,"citation_normalized_percentile":{"value":0.82760143,"is_in_top_1_percent":false,"is_in_top_10_percent":false},"cited_by_percentile_year":{"min":89,"max":96},"biblio":{"volume":"17","issue":"01","first_page":"141","last_page":"154"},"is_retracted":false,"is_paratext":false,"is_xpac":false,"primary_topic":{"id":"https://openalex.org/T11567","display_name":"semigroups and automata theory","score":0.9998999834060669,"subfield":{"id":"https://openalex.org/subfields/1703","display_name":"Computational Theory and Mathematics"},"field":{"id":"https://openalex.org/fields/17","display_name":"Computer Science"},"domain":{"id":"https://openalex.org/domains/3","display_name":"Physical Sciences"}},"topics":[{"id":"https://openalex.org/T11567","display_name":"semigroups and automata theory","score":0.9998999834060669,"subfield":{"id":"https://openalex.org/subfields/1703","display_name":"Computational Theory and Mathematics"},"field":{"id":"https://openalex.org/fields/17","display_name":"Computer Science"},"domain":{"id":"https://openalex.org/domains/3","display_name":"Physical Sciences"}},{"id":"https://openalex.org/T10911","display_name":"Chemical Synthesis and Analysis","score":0.996999979019165,"subfield":{"id":"https://openalex.org/subfields/1312","display_name":"Molecular Biology"},"field":{"id":"https://openalex.org/fields/13","display_name":"Biochemistry, Genetics and Molecular Biology"},"domain":{"id":"https://openalex.org/domains/1","display_name":"Life Sciences"}},{"id":"https://openalex.org/T12029","display_name":"DNA and Biological Computing","score":0.9955000281333923,"subfield":{"id":"https://openalex.org/subfields/1312","display_name":"Molecular Biology"},"field":{"id":"https://openalex.org/fields/13","display_name":"Biochemistry, Genetics and Molecular Biology"},"domain":{"id":"https://openalex.org/domains/1","display_name":"Life Sciences"}}],"keywords":[{"id":"https://openalex.org/keywords/mathematics","display_name":"Mathematics","score":0.7509305477142334},{"id":"https://openalex.org/keywords/automaton","display_name":"Automaton","score":0.7023520469665527},{"id":"https://openalex.org/keywords/two-way-deterministic-finite-automaton","display_name":"Two-way deterministic finite automaton","score":0.6545515060424805},{"id":"https://openalex.org/keywords/deterministic-automaton","display_name":"Deterministic automaton","score":0.6395714282989502},{"id":"https://openalex.org/keywords/regular-expression","display_name":"Regular expression","score":0.565484344959259},{"id":"https://openalex.org/keywords/nondeterministic-finite-automaton","display_name":"Nondeterministic finite automaton","score":0.5549022555351257},{"id":"https://openalex.org/keywords/expression","display_name":"Expression (computer science)","score":0.537492573261261},{"id":"https://openalex.org/keywords/b\u00fcchi-automaton","display_name":"B\u00fcchi automaton","score":0.5087824463844299},{"id":"https://openalex.org/keywords/quotient","display_name":"Quotient","score":0.4911806285381317},{"id":"https://openalex.org/keywords/set","display_name":"Set (abstract data type)","score":0.4902418255805969},{"id":"https://openalex.org/keywords/continuous-automaton","display_name":"Continuous automaton","score":0.4637942910194397},{"id":"https://openalex.org/keywords/timed-automaton","display_name":"Timed automaton","score":0.44728511571884155},{"id":"https://openalex.org/keywords/discrete-mathematics","display_name":"Discrete mathematics","score":0.44618314504623413},{"id":"https://openalex.org/keywords/block-cellular-automaton","display_name":"Block cellular automaton","score":0.42926347255706787},{"id":"https://openalex.org/keywords/finite-state-machine","display_name":"Finite-state machine","score":0.3750166594982147},{"id":"https://openalex.org/keywords/combinatorics","display_name":"Combinatorics","score":0.35145193338394165},{"id":"https://openalex.org/keywords/algorithm","display_name":"Algorithm","score":0.28553926944732666},{"id":"https://openalex.org/keywords/automata-theory","display_name":"Automata theory","score":0.24348604679107666},{"id":"https://openalex.org/keywords/computer-science","display_name":"Computer science","score":0.16267690062522888},{"id":"https://openalex.org/keywords/theoretical-computer-science","display_name":"Theoretical computer science","score":0.12598544359207153}],"concepts":[{"id":"https://openalex.org/C33923547","wikidata":"https://www.wikidata.org/wiki/Q395","display_name":"Mathematics","level":0,"score":0.7509305477142334},{"id":"https://openalex.org/C112505250","wikidata":"https://www.wikidata.org/wiki/Q787116","display_name":"Automaton","level":2,"score":0.7023520469665527},{"id":"https://openalex.org/C139423837","wikidata":"https://www.wikidata.org/wiki/Q243800","display_name":"Two-way deterministic finite automaton","level":5,"score":0.6545515060424805},{"id":"https://openalex.org/C194525867","wikidata":"https://www.wikidata.org/wiki/Q5265707","display_name":"Deterministic automaton","level":3,"score":0.6395714282989502},{"id":"https://openalex.org/C121329065","wikidata":"https://www.wikidata.org/wiki/Q185612","display_name":"Regular expression","level":2,"score":0.565484344959259},{"id":"https://openalex.org/C158008952","wikidata":"https://www.wikidata.org/wiki/Q617295","display_name":"Nondeterministic finite automaton","level":4,"score":0.5549022555351257},{"id":"https://openalex.org/C90559484","wikidata":"https://www.wikidata.org/wiki/Q778379","display_name":"Expression (computer science)","level":2,"score":0.537492573261261},{"id":"https://openalex.org/C165753454","wikidata":"https://www.wikidata.org/wiki/Q1020380","display_name":"B\u00fcchi automaton","level":4,"score":0.5087824463844299},{"id":"https://openalex.org/C199422724","wikidata":"https://www.wikidata.org/wiki/Q41118","display_name":"Quotient","level":2,"score":0.4911806285381317},{"id":"https://openalex.org/C177264268","wikidata":"https://www.wikidata.org/wiki/Q1514741","display_name":"Set (abstract data type)","level":2,"score":0.4902418255805969},{"id":"https://openalex.org/C21720249","wikidata":"https://www.wikidata.org/wiki/Q5165460","display_name":"Continuous automaton","level":5,"score":0.4637942910194397},{"id":"https://openalex.org/C30788636","wikidata":"https://www.wikidata.org/wiki/Q7805517","display_name":"Timed automaton","level":3,"score":0.44728511571884155},{"id":"https://openalex.org/C118615104","wikidata":"https://www.wikidata.org/wiki/Q121416","display_name":"Discrete mathematics","level":1,"score":0.44618314504623413},{"id":"https://openalex.org/C63497236","wikidata":"https://www.wikidata.org/wiki/Q4927188","display_name":"Block cellular automaton","level":5,"score":0.42926347255706787},{"id":"https://openalex.org/C167822520","wikidata":"https://www.wikidata.org/wiki/Q176452","display_name":"Finite-state machine","level":2,"score":0.3750166594982147},{"id":"https://openalex.org/C114614502","wikidata":"https://www.wikidata.org/wiki/Q76592","display_name":"Combinatorics","level":1,"score":0.35145193338394165},{"id":"https://openalex.org/C11413529","wikidata":"https://www.wikidata.org/wiki/Q8366","display_name":"Algorithm","level":1,"score":0.28553926944732666},{"id":"https://openalex.org/C116248031","wikidata":"https://www.wikidata.org/wiki/Q214526","display_name":"Automata theory","level":3,"score":0.24348604679107666},{"id":"https://openalex.org/C41008148","wikidata":"https://www.wikidata.org/wiki/Q21198","display_name":"Computer science","level":0,"score":0.16267690062522888},{"id":"https://openalex.org/C80444323","wikidata":"https://www.wikidata.org/wiki/Q2878974","display_name":"Theoretical computer science","level":1,"score":0.12598544359207153},{"id":"https://openalex.org/C199360897","wikidata":"https://www.wikidata.org/wiki/Q9143","display_name":"Programming language","level":1,"score":0.0}],"mesh":[],"locations_count":1,"locations":[{"id":"doi:10.1142/s021819670700355x","is_oa":false,"landing_page_url":"https://doi.org/10.1142/s021819670700355x","pdf_url":null,"source":{"id":"https://openalex.org/S23260266","display_name":"International Journal of Algebra and Computation","issn_l":"0218-1967","issn":["0218-1967","1793-6500"],"is_oa":false,"is_in_doaj":false,"is_core":true,"host_organization":"https://openalex.org/P4310319815","host_organization_name":"World Scientific","host_organization_lineage":["https://openalex.org/P4310319815"],"host_organization_lineage_names":["World Scientific"],"type":"journal"},"license":null,"license_id":null,"version":"publishedVersion","is_accepted":true,"is_published":true,"raw_source_name":"International Journal of Algebra and Computation","raw_type":"journal-article"}],"best_oa_location":null,"sustainable_development_goals":[],"awards":[],"funders":[],"has_content":{"grobid_xml":false,"pdf":false},"content_urls":null,"referenced_works_count":15,"referenced_works":["https://openalex.org/W1810686855","https://openalex.org/W1966773178","https://openalex.org/W2002089154","https://openalex.org/W2077450865","https://openalex.org/W2084159038","https://openalex.org/W2094985106","https://openalex.org/W2099540492","https://openalex.org/W2103737357","https://openalex.org/W2108142022","https://openalex.org/W2129414328","https://openalex.org/W2912608078","https://openalex.org/W2913383557","https://openalex.org/W4211010176","https://openalex.org/W4285719527","https://openalex.org/W4302339081"],"related_works":["https://openalex.org/W186350370","https://openalex.org/W2522171317","https://openalex.org/W2155870982","https://openalex.org/W2042728676","https://openalex.org/W2091988401","https://openalex.org/W2024315516","https://openalex.org/W2377282071","https://openalex.org/W2393610321","https://openalex.org/W2365495444","https://openalex.org/W1974596900"],"abstract_inverted_index":{"There":[0],"exist":[1],"two":[2],"well-known":[3],"quotients":[4],"of":[5,9,28,39,82,91,98,127,151],"the":[6,17,26,37,52,69,80,89,92,96,99,119,148],"position":[7],"automaton":[8,94,101,150],"a":[10,85,125,152],"regular":[11,128,136],"expression.":[12],"The":[13,42],"first":[14,21,123],"one,":[15,44],"called":[16,51,130],"equation":[18,100,149],"automaton,":[19,54],"was":[20],"introduced":[22],"by":[23,34,58,122],"Mirkin":[24],"from":[25,36],"notion":[27,38],"prebase":[29],"and":[30,48,50,74,77,95,102,144],"has":[31],"been":[32],"redefined":[33],"Antimirov":[35],"partial":[40],"derivative.":[41],"second":[43],"due":[45],"to":[46,110],"Ilie":[47,76],"Yu":[49,78],"follow":[53,93,160],"can":[55,138],"be":[56,139],"obtained":[57],"eliminating":[59],"\u03b5-transitions":[60],"in":[61,84,141],"an":[62],"\u03b5-NFA":[63],"that":[64,104,134,147],"is":[65,106,155],"always":[66,156],"smaller":[67,157],"than":[68,158],"classical":[70],"\u03b5-NFAs":[71],"(Thompson,":[72],"Sippu":[73],"Soisalon\u2013Soininen).":[75],"discussed":[79],"difficulty":[81],"succeeding":[83],"theoretical":[86,120],"comparison":[87],"between":[88],"size":[90,97],"concluded":[103],"it":[105],"very":[107],"likely":[108],"necessary":[109],"realize":[111],"experimental":[112],"studies.":[113],"In":[114],"this":[115],"paper":[116],"we":[117],"solve":[118],"question,":[121],"defining":[124],"set":[126],"expressions,":[129,132],"normalized":[131,140,153],"such":[133],"every":[135],"expression":[137,154],"linear":[142],"time,":[143],"proving":[145],"then":[146],"its":[159],"automaton.":[161]},"counts_by_year":[{"year":2025,"cited_by_count":2},{"year":2023,"cited_by_count":1},{"year":2021,"cited_by_count":1},{"year":2019,"cited_by_count":1},{"year":2017,"cited_by_count":2},{"year":2015,"cited_by_count":1},{"year":2014,"cited_by_count":1},{"year":2013,"cited_by_count":2}],"updated_date":"2026-06-11T09:08:48.828518","created_date":"2025-10-10T00:00:00"}
